In a wide saucepan heat the water, sugar, lemon juice and cinnamon until the sugar dissolves.
Boil gently for several minutes.
Peel the apples and drop immediately into the hot syrup, turning to coat all over.
Poach very, very gently until the apples are just tender but not mushy, turning once.
Drain, arrange in a flameproof dish and keep warm in a low oven.
Meanwhile, boil the syrup furiously until reduced to about 1/4 pint (1 1/2 dl.).
Stir in the apricot jam and butter and, when hot, pour over the apples.
Sprinkle lightly with sugar.
Heat the rum, ignite and pour flaming over the apples.
Serve immediately with thick fresh cream handed separately.